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Product-Mix Decision with a scarce resource (LO4, Loosely adapted from HBS case 198-085, LeHigh Steel). Sylvester's Steel Works is a mini mill that recycles shredded scrap steel into usable products such as alloy (e.g., communication equipment), coils (e.g., appliances), steel bars (e.g., reinforcing concrete), and wire (e.g., cable connectors). Sylvester's starts with a basic feed stock of shredded scrap steel and then melts and purifies the steel via its high-powered electric furnace. The molten metal is next transferred for processing in Sylvester's Cold Rolling Mill (CRM), which is the bottleneck machine in Sylvester's manufacturing process. Management of Sylvester's has provided you with the following data regarding the company's four primary product lines, and the amount of time (in minutes) a pound of each product requires in the Cold Rolling Mill (CRM).

AlloyCoilsSteel BarsWire

Contribution margin per pound $1.40$0.45$0.98 $0.75

Minutes per pound in CRM 0.10 0.030.35 0.30

Sylvester's fixed costs amount to $2,400,000 per year.

a.Suppose the Cold Rolling Mill can be operated for 24,000 minutes per month. What product(s) should Sylvester produce in the coming month? If management follows your production advice, how much profit will Sylvester earn next month?

b.Do you believe the solution you arrived at in part (a) is feasible? What additional data would you require before deciding which product Sylvester's Steel Works should emphasize?

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